A circle with circumference ${6}$ has an arc with a $20^\circ$ central angle. What is the length of the arc?
Solution: The ratio between the arc's central angle ${\theta}$ and $360^\circ$ is equal to the ratio between the arc length ${s}$ and the circle's circumference ${c}$. $\dfrac{{\theta}}{360^\circ} = \dfrac{{s}}{{c}}$ $\dfrac{{20}^\circ}{360^\circ} = \dfrac{{s}}{{{6}}}$ $\dfrac{1}{18} = \dfrac{{s}}{{6}}$ $\dfrac{1}{18} \times {6} = {s}$ $\dfrac{1}{3} = {s}$ ${6}$ ${20^\circ}$ ${\dfrac{1}{3}}$